DIV + MOD
Description
Not so long ago, Vlad came up with an interesting function:
- $f_a(x)=\left\lfloor\frac{x}{a}\right\rfloor + x \bmod a$, where $\left\lfloor\frac{x}{a}\right\rfloor$ is $\frac{x}{a}$, rounded down, $x \bmod a$ — the remainder of the integer division of $x$ by $a$.
For example, with $a=3$ and $x=11$, the value $f_3(11) = \left\lfloor\frac{11}{3}\right\rfloor + 11 \bmod 3 = 3 + 2 = 5$.
The number $a$ is fixed and known to Vlad. Help Vlad find the maximum value of $f_a(x)$ if $x$ can take any integer value from $l$ to $r$ inclusive ($l \le x \le r$).
The first line of input data contains an integer $t$ ($1 \le t \le 10^4$) — the number of input test cases.
This is followed by $t$ lines, each of which contains three integers $l_i$, $r_i$ and $a_i$ ($1 \le l_i \le r_i \le 10^9, 1 \le a_i \le 10^9$) — the left and right boundaries of the segment and the fixed value of $a$.
For each test case, output one number on a separate line — the maximum value of the function on a given segment for a given $a$.
Input
The first line of input data contains an integer $t$ ($1 \le t \le 10^4$) — the number of input test cases.
This is followed by $t$ lines, each of which contains three integers $l_i$, $r_i$ and $a_i$ ($1 \le l_i \le r_i \le 10^9, 1 \le a_i \le 10^9$) — the left and right boundaries of the segment and the fixed value of $a$.
Output
For each test case, output one number on a separate line — the maximum value of the function on a given segment for a given $a$.
Samples
5
1 4 3
5 8 4
6 10 6
1 1000000000 1000000000
10 12 8
2
4
5
999999999
5
Note
In the first sample:
- $f_3(1) = \left\lfloor\frac{1}{3}\right\rfloor + 1 \bmod 3 = 0 + 1 = 1$,
- $f_3(2) = \left\lfloor\frac{2}{3}\right\rfloor + 2 \bmod 3 = 0 + 2 = 2$,
- $f_3(3) = \left\lfloor\frac{3}{3}\right\rfloor + 3 \bmod 3 = 1 + 0 = 1$,
- $f_3(4) = \left\lfloor\frac{4}{3}\right\rfloor + 4 \bmod 3 = 1 + 1 = 2$
As an answer, obviously, $f_3(2)$ and $f_3(4)$ are suitable.